Question

It is important that the force required to extract a cork from a wine bottle not have a large standard deviation. Years of production and testing indicate that the no. 9 corks in Applied Example 6.13 (p. 285) have an extraction force that is normally distributed with a standard deviation of 36 Newtons. Recent changes in the manufacturing process are thought to have reduced the standard deviation.
a. What would be the problem with the standard deviation being relatively large? What would be the advantage of a smaller standard deviation? A sample of 20 randomly selected bottles is used for testing.

b. Is the preceding sample sufficient to show that the standard deviation of extraction force is less than 36.0 Newtons, at the 0.02 level of significance? During a different testing, a sample of eight bottles is randomly selected and tested.

c. Is the preceding sample sufficient to show that the standard deviation of extraction force is less than 36.0 Newtons, at the 0.02 level of significance?
d. What effect did the two different sample sizes have on the calculated test statistic in parts b and c? What effect did they have on the p-value or critical value? Explain.
e. What effect did the two different sample standard deviations have on the answers in parts b and c? What effect did they have on the p-value or critical value? Explain.